Negative feedback control is essential to make biological systems stable to internal and external perturbations. It is used to regulate everything from body temperature to gene expression, and its failure causes a range of human disorders. But our understanding of feedback in biology is incomplete and incoherent. Most systematic theoretical approaches are based on deterministic kinetics, poorly suited for microscopic cellular events, and few systems allow accurate experimental measurements of the numbers of individual molecules in a given cell. Prior work focused so closely on the details of each system that general guiding principles have been overlooked, in turn making detailed analysis difficult. We propose to address these problems by developing new mathematical approaches and systematically applying our novel experimental molecule counting assays to simple model systems. Our preliminary theory demonstrates hard limits on the ability of negative feedback to suppress fluctuations in cellular systems, and general frustration trade-offs where reducing one type of variation instead amplifies another. It also suggests creative mechanisms that minimize these problems, and remarkably enough, we have now found examples of these in biology. We propose to extend the individual theorems by integrating central concepts from statistical physics and control theory into a novel coherent framework that makes it possible to make exact quantitative statements about strongly nonlinear and exotic systems. The theory is also used to motivate, design and interpret quantitative experiments for two systems that promote virulence and drug resistance in Escherichia coli. We focus on replication control of bacterial plasmids, where noise suppression is essential. The unmatched tractability of plasmids allows us to systematically vary control loop properties and rigorously test the general theorems. We will compare these results with those for stress response sigma factor RpoS, where we believe negative feedback may instead enhance variation. Our studies will help lay the groundwork for effective studies of randomness in biology: where it comes from, how it is controlled, what limits physics sets on how biological systems suppress noise, and the creative ways that biological systems exploit apparent loopholes in those limits. We believe this will expose new principles that will help us understand how biological systems evolved, and how they function in health and disease particularly in systems that promote drug resistance and virulence in bacteria.